Everyone agrees that the Jaguar E-Type is a beautiful car. But it’s 55 years since it first came out – and that’s 55 years in which the motor industry, Jag included, has been getting relentlessly better at what it does.

The result is that while there’s still not a lot that can claim to look as good, there’s no shortage of modern cars that are better to drive. Indeed, anything that’s not better to drive than a car from five and a half decades ago deserves to be shot.

But what if Jag was building the E-Type today? What would it be like?

It would be like this.

Eagle E-Types doesn’t just restore and sell originals. It also develops them into what they might have become.

This is the latest masterpiece to appear from its workshops. You’re looking at the Eagle Low Drag GT.

Note the use of the word ‘the’, not ‘a’. The car in these pictures is the only one in the world. If you want one like it, it’ll be finished in spring 2017 and cost you £650,000.

The Low Drag Coupe was an E-Type with revised, more aerodynamic bodywork. It didn’t achieve any great success on the racetrack, but over time it became a bit of a sought-after rarity.

Eagle puts that bodywork to rather greater effect. It’s attached to a chassis that’s 2” longer, to allow better leg room, and beneath it is an array of engineering to turn you weak at the knees.

Jag’s iconic twin-cam in-line six, for example, now has fuel injection and an ally block. More than just a warm-over, then. It’s running a longer stroke, too, as well as a wider bore, taking it out to 4.7 litres and up to 345bhp.

The gearbox behind it has Eagle’s own case and workings, and there’s a sticky diff behind the back wheels. Lots of aluminium here, too – which all helps to keep the car to a supremely light 1038kg.

Underneath, it all sounds very race-bred, with AP Racing brakes and Ohlins shocks.

But this isn’t a stripped out track-tool. Au contraire, while the dash switches are original they now operate things like climate control. You get PAS, too, as well as a properly luxurious cabin.

That matters because fast but refined cruising is important in an E-Type. And you can chat away with ease, even when hammering along at twice the speed limit. It rides with immense composure.

As for handling, the answer’s yes. You just have to decide what the question is. The adjustable shocks and anti-roll bar mean you can set it up pretty much any way you want it; however that is, the steering will keep you informed via the wood-rimmed wheel of exactly what’s going on at the front wheels.

Thing is, it grips and handles like no E-Type you’ll ever have driven (unless you’ve had your hands on an Eagle-built example before). And it goes like no other E-Type, too, as well as changing gear with a perfect mechanical precision.

It is, to all intents and purposes, exactly what we mused on above. If Jaguar was developing a new E-Type from scratch, this is what it would be like. Well, this is what the ‘R’ model would be like.

Will there be more than one Low Drag GT? If the demand is there, yes. It’s hard to imagine that Britain’s super-rich will be able to resist for long.